Which of the following characteristic features match(es) with the crystal systems: cubic and rhombohedral?

Options

A. Both have the cell parameters a = b = c and `alpha=beta=gamma`
B. Both belong to different crystal systems
C. Both have only two crystallographic angles of `90^(@)`
D. Both belong to same crystal system

Answer

To solve the question regarding the characteristic features of the cubic and rhombohedral crystal systems, we need to analyze the properties of each system step by step.

### Step 1: Understanding the Cubic Crystal System
- **Characteristic Features**: In the cubic crystal system, all three edges (a, b, c) are equal in length (a = b = c), and all angles (α, β, γ) are equal to 90 degrees.
- **Conclusion**: The cubic system has equal edge lengths and right angles.

### Step 2: Understanding the Rhombohedral Crystal System
- **Characteristic Features**: In the rhombohedral crystal system, all three edges are also equal in length (a = b = c), but the angles (α, β, γ) are equal to each other but not equal to 90 degrees (typically they are less than or greater than 90 degrees).
- **Conclusion**: The rhombohedral system has equal edge lengths, but the angles are not right angles.

### Step 3: Comparing the Two Systems
- **Equal Edge Lengths**: Both cubic and rhombohedral systems have equal edge lengths.
- **Angle Comparison**: The cubic system has angles of 90 degrees, while the rhombohedral system has equal angles that are not 90 degrees.

### Step 4: Evaluating the Statements
1. **Statement 1**: Both systems have equal edge lengths. (True for both)
2. **Statement 2**: Both systems have angles that are equal to each other. (True for both)
3. **Statement 3**: Both systems have angles of 90 degrees. (False for rhombohedral)
4. **Statement 4**: Both belong to the same crystal system. (False)

### Final Conclusion
- The correct characteristic features that match with both cubic and rhombohedral systems are:
- Both have equal edge lengths.
- Both have angles that are equal to each other.